3

Part of 2004 Korea National Olympiad

Problems(1)

KMO second round #3

Source:

Positive real numbers,

a_1, .. ,a_6

a_1^2+..+a_6^2=2

. Think six squares that has side length of

a_i

i=1,2,\ldots,6

). Show that the squares can be packed inside a square of length

2

, without overlapping.

geometryrectanglegeometry unsolved